Question

axis symmetry, graph max or min value, domain, range and all intervals where function increases or decreases. f(x)=5(x-3)^2+6 f(x)=-7(x-8)^2+1 f(x)=-6(x+4)^-8 f(x)=2(x+2)^2+9

Answer 1

In general if equation of parabola of the form is:

Where (h,k) is vertex of parabola

x = h is axis of symmetry.

If a is positive then parabola is opening upward.

Then vertex is minimum of that function.

If a is negative then parabola is opening downward.

Then vertex is maximum of that function.

Given function is:

On comparing

a = 5 , h = 3, k = 6

So vertex of parabola is (3,6)

Axis of symmetry is

a is positive then then it is opening upward parabola.

So there is minimum of function at vertex of parabola.

So function has minimum at x = 3 and minimum value is 6.

Parabolic function define for all real value of x.

So domain is set of all real value of x.

Range of function is:

Derivative of function is:

Function increases where

So function increases for

2.

Given function is:

On comparing

a = -7 , h = 8, k = 1

So vertex of parabola is (8,1)

Axis of symmetry is

a is negative then then it is opening downward parabola.

So there is maximum of function at vertex of parabola.

So function has maximum at x = 8 and maximum value is 1.

Parabolic function define for all real value of x.

So domain is set of all real value of x.

Range of function is:

Derivative of function is:

Function increases where

So function increases for

3.

Given function is:

On comparing

a = -6 , h = -4, k = -8

So vertex of parabola is (-4,-8)

Axis of symmetry is

a is negative then then it is opening downward parabola.

So there is maximum of function at vertex of parabola.

So function has maximum at x = -4 and maximum value is -8.

Parabolic function define for all real value of x.

So domain is set of all real value of x.

Range of function is:

Derivative of function is:

Function increases where

So function increases for